1. Field of the Invention
This invention relates to quantum computing and, in particular, to superconducting quantum computing systems.
2. Description of Related Art
Research on what is now called quantum computing traces back to Richard Feynman. See, e.g., R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). He noted that quantum systems are inherently difficult to simulate with classical (i.e., conventional, non-quantum) computers, but that this task could be accomplished by observing the evolution of another quantum system. In particular, solving a theory for the behavior of a quantum system commonly involves solving a differential equation related to the system""s Hamiltonian. Observing the behavior of the system provides information regarding the solutions to the equation.
Further efforts in quantum computing were initially concentrated on building the formal theory or on xe2x80x9csoftware developmentxe2x80x9d or extension to other computational problems. Discovery of the Shor and Grover algorithms were important milestones in quantum computing. See, e.g., P. Shor, SIAM J. of Comput. 26, 1484 (1997); L. Grover, Proc. 28th STOC, 212 (ACM Press, New York, 1996), which is hereby incorporated by reference in its entirety; and A. Kitaev, LANL preprint quant-ph/9511026, which is hereby incorporated by reference in its entirety. In particular, the Shor algorithm permits a quantum computer to factorize large natural numbers efficiently. In this application, a quantum computer could render obsolete all existing xe2x80x9cpublic-keyxe2x80x9d encryption schemes. In another application, quantum computers (or even a smaller-scale device such as a quantum repeater) could enable absolutely safe communication channels where a message, in principle, cannot be intercepted without being destroyed in the process. See, e.g., H. J. Briegel et al., preprint quant-ph/9803056 and references therein, which is hereby incorporated by reference in its entirety. Showing that fault-tolerant quantum computation is theoretically possible opened the way for attempts at practical realizations. See, e.g., E. Knill, R. Laflamme, and W. Zurek, Science 279, 342 (1998), which is hereby incorporated by reference in its entirety.
Quantum computing generally involves initializing the states of N qubits (quantum bits), creating controlled entanglements among them, allowing these states to evolve, and reading out the states of the qubits after the evolution. A qubit is conventionally a system having two degenerate (i.e., of equal energy) quantum states, with a non-zero probability of being found in either state. Thus, N qubits can define an initial state that is a combination of 2N classical states. This initial state undergoes an evolution, governed by the interactions that the qubits have among themselves and with external influences. This evolution of the states of N qubits defines a calculation or, in effect, 2N simultaneous classical calculations. Reading out the states of the qubits after evolution is complete determines the results of the calculations.
Several physical systems have been proposed for the qubits in a quantum computer. One system uses molecules having degenerate nuclear-spin states. See N. Gershenfeld and I. Chuang, xe2x80x9cMethod and Apparatus for Quantum Information Processing,xe2x80x9d U.S. Pat. No. 5,917,322, which is hereby incorporated by reference in its entirety. Nuclear magnetic resonance (NMR) techniques can read the spin states. These systems have successfully implemented a search algorithm, see, e.g., M. Mosca, R. H. Hansen, and J. A. Jones, xe2x80x9cImplementation of a quantum search algorithm on a quantum computer,xe2x80x9d Nature 393, 344 (1998) and references therein, which is hereby incorporated by reference in its entirety, and a number-ordering algorithm, see, e.g., L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, xe2x80x9cExperimental realization of order-finding with a quantum computer,xe2x80x9d preprint quant-ph/0007017 and references therein, which is hereby incorporated by reference in its entirety. (The number-ordering algorithm is related to the quantum Fourier transform, an essential element of both Shor""s factoring algorithm and Grover""s algorithm for searching unsorted databases.) However, expanding such systems to a commercially useful number of qubits is difficult. More generally, many of the current proposals will not scale up from a few qubits to the 102xcx9c103 qubits needed for most practical calculations.
Further, current methods for entangling qubits are susceptible to loss of coherence. Entanglement of quantum states of qubits can be an important step in the application of quantum algorithms. See for example, P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997), which is hereby incorporated by reference in its entirety. Current methods for entangling phase qubits require the interaction of the flux in each of the qubits, see Yuriy Makhlin, Gerd Schon, Alexandre Shnirman, xe2x80x9cQuantum state engineering with Josephson-junction devices,xe2x80x9d LANL preprint, cond-mat/0011269 (November 2000), which is hereby incorporated by reference in its entirety. This form of entanglement is sensitive to the qubit coupling with surrounding fields, which cause decoherence and loss of information.
As discussed above, currently proposed methods for readout, initialization, and entanglement of a qubit involve detection or manipulation of magnetic fields at the location of the qubit, which make these methods susceptible to decoherence and limits the overall scalability of the resulting quantum computing device. Thus, there is a need for an efficient quantum register where decoherence and other sources of noise is minimized but where scalability is maximized.
In accordance with the present invention, a quantum register is presented. A quantum register according to the present invention includes one or more finger SQUID qubit devices.
A finger SQUID qubit device according to an embodiment of the present invention can include a superconducting loop and a superconducting finger, wherein the superconducting finger extends from the superconducting loop towards the interior of the superconducting loop. The superconducting loop may have multiple branches. Each branch may have a Josephson junction. The Josephson junction may be a grain boundary junction. The finger SQUID qubit device may have leads capable of conducting current to and from the superconducting loop. The leads may be capable of conducting supercurrent.
When structures are referred to as xe2x80x9csuperconductingxe2x80x9d herein, they are fabricated from a material capable of superconducting and so may superconduct under the correct conditions. For example, the superconducting loop and superconducting finger may be fabricated from a d-wave superconductor and so will superconduct under appropriate physical conditions. For example, the superconducting loop and finger will superconduct at an appropriate temperature, magnetic field, and current. However, the xe2x80x9csuperconducting loopxe2x80x9d will not superconduct under other physical conditions. For example, when the temperature is too high, the superconducting loop will not be in a superconducting state. Additionally, structures such as superconducting SETs and other superconducting switches mentioned herein are capable of superconducting under appropriate physical conditions.
A device in accordance with an embodiment of the invention generally operates at a temperature such that thermal excitations in the superconducting crystal lattice are sufficiently suppressed to perform quantum computation. In some embodiments of the invention, such a temperature can be on the order of 1K or less. In some other embodiments of the invention, such a temperature can be on the order of 50 mK or less. Furthermore, other dissipative sources, such as magnetic fields for example, should be minimized to an extent such that quantum computing can be performed with a minimum of dissipation and decoherence.
The material capable of superconducting used in embodiments of the invention may be a material that violates time-reversal symmetry. For example, a d-wave superconductor may be used. For example, the d-wave superconductors YBa2Cu3O7xe2x88x92x, Bi2Sr2Canxe2x88x921CunO2n+4, Tl2Ba2CuO6+x, and HgBa2CuO4 may be used.
According to some embodiments of the present invention, the superconducting finger includes a Josephson junction, such that a mesoscopic island is separated from the rest of the superconducting finger by the junction.
For the Josephson junctions in the branches or the finger, the orientation of the superconducting order parameter on one side of the Josephson junction may be different from the orientation of the superconducting order parameter on the other side of the Josephson junction. For example, the orientation of the superconducting order parameter in the region above the Josephson junction may be rotated approximately 45 degrees with respect to the orientation of the superconducting order parameter below the Josephson junction. Other non-zero misorientations may be used to form a grain boundary Josephson junction. The orientation of the superconducting order parameter in the region above the Josephson junction may be rotated with respect to the orientation of the grain boundary. The orientation of the superconducting order parameter in the region below the Josephson junction may be rotated with respect to the orientation of the grain boundary.
The orientation of the superconducting order parameter is related to the orientation of the crystal lattice of the superconductor. Therefore, the orientation of the superconducting order parameter is generally controlled by controlling the orientation of the crystal lattice. For example, bi-epitaxial fabrication methods can be used to achieve the desired orientation of the superconducting order parameter in regions adjacent to the grain boundary. Alternately, bi-crystal fabrication methods may be used to achieve the desired orientation of the superconducting order parameter in regions adjacent to the grain boundary.
In a qubit device as presented in embodiments of the current invention, the superconducting finger, including the mesoscopic island region, forms a qubit as explained below, and the surrounding superconducting loop allows interaction with and control of the qubit. The loop and finger together, then, can be referred to as the qubit device.
If the order parameter in a first region of the loop, from which the finger extends, has a phase of "PHgr", a phase "PHgr"xc2x1xcex94"PHgr" is accumulated in the order parameter across the Josephson junction in the finger. The sign of the phase change depends on the direction of circulation of the ground state supercurrent. The qubit has two bistable phase states, corresponding to the change in phase +xcex94"PHgr" or xe2x88x92xcex94"PHgr" of the order parameter across the Josephson junction in the finger. Therefore, the region of qubit device including the finger and the region of the loop from which the finger extends can then be referred to as the qubit. Additionally, the two bi-stable phase states form the basis states of the qubit can be referred to as the |+xcex94"PHgr" greater than  and |xe2x88x92xcex94"PHgr" greater than  states, with measurable qubit phase change values of +xcex94"PHgr" and xe2x88x92xcex94"PHgr". For operation as a qubit, these states are referred to as the basis states |0 greater than  and |1 greater than .
Although the measurable values of the qubit phase change are equal to +xcex94"PHgr" or xe2x88x92xcex94"PHgr", in a quantum computing device the qubit phase is generally not directly measured. The term xe2x80x9cmeasurable valuexe2x80x9d here refers to the quantum mechanical use of the term, where a measurable value is a physical attribute of a system that can be described by an operator in the system""s Hilbert space (such as energy, position or momentum). In making an actual measurement, a current may be provided through a qubit device and a resulting voltage across the qubit device will be measured. The measured voltage will depend on the state of the qubit. That is, the measured voltage will be different if the qubit is in the basis state corresponding to a measurable value of the qubit phase difference of +xcex94"PHgr" than if the qubit is in the basis state corresponding to a measurable value of the qubit phase difference of xe2x88x92xcex94"PHgr".
In some embodiments of the current invention, a control system is included. The control system may provide current to the superconducting leads of a qubit device as described above. The control system may also measure a voltage change across the leads, may convert a measured voltage change to a qubit value, may store the qubit value, and/or may store the measured voltage change. The qubit value corresponds to one of the two qubit basis states described above, but in this example the quantities +xcex94"PHgr" and xe2x88x92xcex94"PHgr" are not directly measured. Instead, the qubit value may be stored as a voltage, as a 1 or a 0, or as some other parameter.
In some embodiments of the invention, the orientation of the grain boundary forming the junction can be tilted with respect to the orientation of the branches of the superconducting loop. This can alter the phase of the superconducting ground state beyond the shift caused by the misorientation of the superconductor crystal lattice with the corresponding grain boundary. Alternately, one or more of the branches of the superconducting loop can be tilted with respect to the orientation of the grain boundaries forming the grain boundary Josephson junctions.
Further, the branches or the grain boundaries forming the Josephson junctions in the branches can have a different tilt angle with respect to one another, such that the junctions in each branch can correlate with a different ground state phase difference. Again, this ground state phase difference may be accompanied by a ground state phase difference caused by the misorientation of the superconductor crystal lattice with the corresponding grain boundary. Furthermore, said ground state phase difference across the junctions in the branches of the superconducting loop can be different from the ground state phase difference across the junction isolating the island on the superconducting finger. The ground state phase difference can depend on the direction of the grain boundary with respect to the orientation of the superconducting order parameter above and below the grain boundary or on direction of the grain boundary with respect to the branch.
In some embodiments of the invention, a link may be provided between the superconducting loop and the mesoscopic island of a qubit device as described above. The link may include a switching mechanism. The switching mechanism may be a coherent switching mechanism such as a parity key or superconducting SET.
In some embodiments of the invention, a link may be provided between the mesoscopic island of a qubit device as described above and a ground. The link may include a switching mechanism. The switching mechanism may be a coherent switching mechanism such as a parity key or superconducting SET.
In some embodiments of the quantum register, the magnitude of xcex94"PHgr" may differ between qubit devices depending on the characteristics of each qubit device. Such a difference does not affect the ability of the qubit devices to be used in quantum computing. Further, by controlling the fabrication of the qubit devices so that differences between devices are minimal, the magnitude of the qubit phase may only slightly vary among devices. However, even though the magnitude of the qubit phase corresponding to one of the qubit basis states may differ among devices, for each particular qubit device there are doubly degenerate basis states as described above which correspond to two measurable values of qubit phase.
In some embodiments of the current invention, a quantum register includes multiple qubit devices. Each qubit device may include one or more qubits. In an embodiment where a quantum register includes a first qubit device and a second qubit device, the first qubit device may be coupled to the second qubit device by providing a coupling link between a mesoscopic island of the first device and a mesoscopic island of a second device. The coupling link can include a coupling switch, such that when the coupling switch is in the closed position it conducts current. In some embodiments, the coupling link can coherently conduct supercurrent. The coupling switch may be a superconducting SET or a parity key.
In some embodiments of the invention, a quantum register includes one or more superconducting loops. Each superconducting loop may include multiple fingers extending from the loop toward the interior of the loop. Each finger may include a Josephson junction separating a mesoscopic island from the rest of the finger.
In some embodiments of the invention, a quantum register may include a plurality of superconducting loops, where each loop has a finger extending from the loop towards its interior. Each finger may have a Josephson junction separating a mesoscopic island from the rest of the finger.
In some embodiments of the invention, a method of performing a calculation with a quantum computer may include providing a quantum register. The quantum register may include multiple qubit devices as described above. The method of performing a calculation may include initializing the qubit devices to one of the qubit basis states. The method may include coupling one of the qubit devices to another of the devices, so that the quantum states of each of the qubit devices are entangled. The method may include reading the result of the calculation. Reading the result of the calculation may include collapsing the qubit wavefunction into one of its basis states. The method may include storing the results of the calculation in a memory.
Embodiments of the invention can include a method for initializing a qubit. The method can include providing a qubit device as described above, where the qubit has two basis states, |+xcex94"PHgr" greater than and |xe2x88x92xcex94"PHgr" greater than . The method can include initializing the qubit by setting the qubit phase to one of the two ground state values. The state of the qubit can be localized to a single ground state by connecting the mesoscopic island of the qubit device to a ground. Alternately, the qubit state can be set by coupling the mesoscopic island of the qubit device to the superconducting loop of the qubit device. The qubit state may be set by driving a bias current across the leads of the superconducting loop.
Embodiments of the invention can include performing an entanglement operation. An entanglement operation may be performed by coupling two or more qubit devices. For example, an entanglement operation may be performed by providing a first qubit device and a second qubit device as described above, then coupling the first qubit device to the second qubit device. The first qubit device may be coupled to the second qubit device by providing a link between the mesoscopic island of the first qubit device and the mesoscopic island of the second qubit device. The link may include a coherent superconducting switch. The coherent superconducting switch can be a superconducting SET or a parity key. In another embodiment, the first qubit device can be coupled to the second qubit device by providing a superconducting loop between the first qubit device and the second qubit device. The superconducting loop can include a switch such that when the switch is closed the superconducting loop is inductively coupled to the first qubit and the second qubit.
Multiple qubits may be entangled by coupling as described above. For example, a first qubit device may be coupled to a second qubit device as described above. Additionally, the first qubit device may be coupled to a third qubit device. The first qubit device may be coupled to the second qubit device and the third qubit device at the same time. The multiple qubit devices may be arranged in a one-dimensional array, a two-dimensional array, or a three-dimensional array.
Some embodiments of the invention include a method for performing a bias operation on a qubit. The method can include providing a qubit device as described above. The method can further include linking the mesoscopic island of the qubit device to the superconducting loop of the qubit device. The linking can be accomplished using a coherent switching mechanism. The coherent switching mechanism can be a superconducting SET or a parity key.
In some embodiments of the current invention, a method for performing a bias operation can include providing a qubit device as described above. The method can include driving a bias current across the leads of the qubit device. Driving the current in a first direction can bias the qubit to one of the two qubit basis states, while driving the current in the opposite direction can bias the qubit to the other of the two qubit basis states.
In some embodiments of the current invention, a method of reading out the state of a qubit device can include providing a qubit device as described above. The method may include coupling the mesoscopic island of the qubit device to the superconducting loop of the qubit device. The method may further include driving a bias current through the leads of the qubit device. The method may include measuring a voltage change across the leads of the qubit device. The method may include storing the measured voltage change or storing a qubit value corresponding to the measured voltage change in a memory.
In some embodiments of the current invention, a method of reading out the state of a qubit includes providing a qubit device as described above. The method may further include grounding the qubit device. The method may include applying a current across the leads of the qubit device and measuring a voltage change across the leads of the qubit device, where the voltage change may differ depending on which of the two basis states the qubit is in. The method may include storing the measured voltage change or storing a qubit value corresponding to the measured voltage change in a memory. The qubit value may be a voltage, a 0 or a 1, or some other parameter that represents the basis state of the qubit, which is not directly measured in this example.
In some embodiments, a method of grounding a qubit includes providing a qubit device as described above. The method may further include connecting the mesoscopic island of the qubit device to a ground.
In some embodiments, a method of grounding a qubit device includes providing a qubit device as described above. The method may further include driving a current across the leads of the qubit device.
In some embodiments of the invention, a method for initializing the state of a quantum register may include initializing the state of each qubit in the register. The method may further include grounding all of the qubits in the quantum register. The method may further include driving a current across the leads of each of the qubit devices, in parallel or in series.
In some embodiments of the invention, a method for applying quantum gates using the quantum register may include performing bias operations or entanglement operations on one or more qubits in parallel or in series.
In some embodiments of the invention, a method for reading out the state of a quantum register may include performing a readout operation on each of the qubits in the quantum register in parallel or in series.
These and other embodiments are further described below with respect to the following figures.